In comparison to other light sources, lasers can produce highly coherent optical is waves with a well defined and stable optical frequency. An ideal single mode laser would produce a perfectly monochromatic optical field with amplitude and frequency that are constant in time. In practice, the amplitude and frequency of an optical wave produced by even the best single mode lasers display small fluctuations in their amplitude and frequency, known as amplitude noise (or intensity noise) and frequency noise (or phase noise). Frequency and phase noises are related inasmuch as frequency is the time derivative of phase.
Optical field fluctuations result partly from variations in the laser structure and excitation. For example, variations in the power provided to the gain medium to excite atoms or molecules to a higher energy level can translate into amplitude and phase noise in the optical field produced by the laser. Amplification dynamics can exacerbate these fluctuations at some frequencies. For example, Er-doped fiber lasers (EDFL) typically present a resonance peak in intensity noise at frequencies of a few hundreds of kilohertz. Likewise, thermal fluctuations and vibrations can alter the geometry and the optical path length of an optical resonator, thus modifying the resonance conditions and adding frequency noise to the optical field. Such fluctuations resulting from variations in laser structure and excitation are sometimes referred to as technical noise.
Fundamental quantum noise also affects the laser field. Albeit much weaker than stimulated emission, spontaneous emission still contributes a random component to the laser field that translates into intensity and phase noise. Optical losses, either through absorption, scattering or coupling, also add a random component to the to optical field. From a quantum point of view, an optical loss represents an average probability of a photon being lost, random fluctuations around this average value being allowed.
Measures can be taken to stabilize the laser structure and reduce the associated technical noise. However, quantum noise cannot be reduced below a fundamental limit, which determines the narrowest linewidth achievable with a given laser known as the Schawlow-Townes limit. This limit is found to scale as the inverse of the total optical power produced by the laser, including power lost by absorption and scattering, and as the square of the cold cavity linewidth, i.e. the linewidth determined by the cavity length and round trip loss without gain. It is usually the case that technical noise dominates quantum noise and leads to a laser linewidth sizably larger than the Schawlow-Townes limit.
Intensity and phase noise affecting an optical field are usually treated as stationary random variables with statistical properties that do not vary in time. Such variable is characterized in the frequency domain by a power spectral density (PSD), taken as the Fourier transform of its autocorrelation function. FIG. 1 (PRIOR ART) presents frequency noise PSDs measured on an EDFL and a distributed feedback (DFB) semiconductor laser. The frequency noise PSD is expressed in Hz2/Hz. The statistical variance of the laser frequency can be calculated from the PSD according to
                                          σ            freq            2                    =                                    ∫              0              ∞                        ⁢                                                            S                  freq                                ⁡                                  (                  f                  )                                            ⁢                              ⅆ                f                                                    ,                            (        1        )            where Sfreq is the frequency noise PSD and f is the frequency. As seen in FIG. 1, both lasers display a frequency noise PSD with a 1/f variation at low frequencies, which results from technical noise. A floor of white frequency noise at high frequencies that results from quantum noise is clearly visible in the case of the DFB semiconductor laser. This strong white noise component can be explained by a number of factors. The resonator of a semiconductor laser is typically very short and optical loss by absorption and scattering found therein are sizable, two conditions that exacerbate quantum noise. Moreover, gain fluctuations resulting from spontaneous emission are accompanied by fluctuations in the index of refraction of the semiconductor material. Not only does spontaneous emission add a random component to the optical field, it also affects the phase of the coherent component of the optical field via a random perturbation of the optical path within the laser resonator.
Semiconductor lasers present many advantages over other lasers. They are the most efficient, giving more watts of optical output power per watt of electrical power. They are small, lightweight, rugged and insensitive to vibrations by virtue of their monolithic construction. In comparison to other solid-state lasers, single-mode semiconductor lasers display a relatively small intensity noise, with a resonance peak occurring typically at a few GHz. They are cheap and available at many wavelengths, including at 1.5 micron for optical fiber telecommunications and sensing. So-called Integrated Tunable Laser Assemblies (ITLA), based on semiconductor lasers, are commercially available that can provide single-mode laser light over the whole C-band of telecommunications. However, the high level of white frequency noise in semiconductor lasers disqualifies them for some high-end applications, such as high-sensitivity optical fiber sensing, high-resolution range finding, RF photonics, next generation optical telecommunications networks and the like.
Various means have been considered to improve the frequency noise of semiconductor lasers. As aforementioned, the quantum-noise limited linewidth scales inversely to the total optical power. A reduction in white frequency noise is thus expected by running a laser at a higher output power. Likewise, the quantum-noise limited linewidth scales as the square of the cold cavity linewidth. Since the cold cavity linewidth scales inversely to the cavity length, a reduction in white frequency noise is also expected when increasing the cavity length. An increase in cavity length is usually achieved by using an external cavity with one or more reflectors separate from the semiconductor gain medium. Referring to Bartolo et al. [“Characterization of a low-phase-noise, high-power (370 mW), external-cavity semiconductor laser”, Naval Research Laboratory, NRUMR/5670-10-9272, 2010], an external cavity semiconductor laser producing a low white frequency noise was demonstrated. Bartolo et al used a special semiconductor high-power amplifier, which allowed the laser to produce a single-mode output power of up to 370 mW. The external cavity used as reflector a fiber Bragg grating (FBG), which was coupled to the semiconductor amplifier by a lensed fiber. The combined length of the gain medium and the FBG reflector reached nearly 8 inches. The measured frequency noise was within a factor of two from that of a fiber laser, with no apparent white noise floor at frequencies up to 10 MHz. Such a system is fairly complex and presents many disadvantages. The monolithic nature of the semiconductor laser is lost and an increased sensitivity to vibrations ensues. Antireflection coatings are required on the end faces of the semiconductor gain medium to impede laser oscillation in the absence of the external cavity mirrors. Otherwise, coupled cavities are created and the spectral behavior of the laser becomes highly sensitive to the optical phase of the feedback provided by external mirrors. Moreover, cavity lengthening reduces the frequency spacing between longitudinal modes so that narrow band filtering becomes necessary to maintain the single-mode oscillation of the laser. When tuned in frequency, such a laser is prone to mode-hopping, i.e. sudden jumps between neighboring modes of oscillation.
The frequency of emission of a semiconductor laser is known to depend on the injection current. The frequency noise of such a laser can thus be reduced by an appropriate feedback signal to the injection current driving it. Reference can for example be made to M. Ohtsu and S. Kotajima, “Linewidth reduction of a semiconductor laser by electrical feedback”, IEEE J. Quantum Electron. QE-21(12), 1905 (1985), for an explanation of this approach. To determine the feedback signal, a frequency discriminator, i.e. an optical filter with a steep spectral transition is used to translate frequency fluctuations of incoming light into intensity fluctuations. The intensity fluctuations are detected to provide an electrical signal mirroring the frequency fluctuations. A feedback signal deduced from this electrical signal is then is applied to compensate for these fluctuations. An example of such system is illustrated in FIG. 2 (PRIOR ART). In this example, a Fabry-Perot interferometer constituted of two highly reflective fiber Bragg gratings that are π-shifted with regards to one another was used as a discriminator. FIG. 3 shows the apodisation profile of the discriminator. As known in the art, such a device can be designed to reflect light over a spectral range of tens of GHz, except for a narrow band transmission peak in the middle of this spectral range. The spectral response of the interferometer is illustrated in FIGS. 4A and 4B, showing the narrow transmission peak (tens of MHz) surrounded by a wide reflection range. Frequency discrimination is achieved when the laser emission is locked spectrally to the side of the transmission peak. A limiting form of this all-fiber interferometer is a FBG with a π-phase shift in the middle
FIG. 5 (PRIOR ART) compares the PSD of the frequency noise of a DFB semiconductor laser used in a system such as shown in FIG. 2, both with and without activating the feedback loop. As shown, the feedback loop approach allows a sizable frequency noise reduction up to a frequency of about 1 MHz. However, this approach does not reduce frequency noise at higher frequencies.
The above methods rely on modifying the behavior of a semiconductor laser, either by changing its structure or its excitation. Another approach consists in acting on the laser output instead, through optical filtering. A noisy laser has a wider linewidth of emission than a quiet laser. It is thus expected that narrowing down the spectrum of a laser output by optical filtering reduces the noise affecting this laser output. The following expression represents an optical field with an optical carrier frequency fc, which is affected by a single frequency phase noise component of frequency fn, i.e.Eoptical(f)=ej(2πfct+Δφ sin(2πfnt)).  (2)This expression can be approximated as
                                          E            optical                    ⁡                      (            f            )                          ≈                              ⅇ                          j              ⁢                                                          ⁢              2              ⁢              π              ⁢                                                          ⁢                              f                c                            ⁢              t                                +                                    Δϕ              2                        ⁢                          ⅇ                                                j2π                  ⁡                                      (                                                                  f                        c                                            +                                              f                        n                                                              )                                                  ⁢                t                                              -                                    Δϕ              2                        ⁢                                          ⅇ                                                      j2π                    ⁡                                          (                                                                        f                          c                                                +                                                  f                          n                                                                    )                                                        ⁢                  t                                            .                                                          (        3        )            where noise amplitude Δφ is small. The phase noise thus generates a sideband on each side of said optical carrier frequency, these sidebands being separated from the carrier frequency by frequency fn, the amplitude of said sidebands being directly determined by the amplitude of the phase noise. As known in the art, under these conditions, attenuating the optical spectrum at frequencies fc±fn with a pass band optical filter produces the same attenuation of phase noise (and frequency noise) at frequency fn.
A few experimental demonstrations of semiconductor laser frequency noise reduction by optical filtering have been published by HALD et al. [“Efficient suppression of diode-laser phase noise by optical filtering”, J. Opt. Soc. Am. B 22(11), 2338 (2005)] and NAZAROVA et al. [“Low-frequency-noise diode laser for atom interferometry”, J. Opt. Soc. Am. B 25(10), 1632 (2008)]. Bulk Fabry-Perot interferometers with linewidth close to 9 kHz were used as the optical filter. The well known Pound-Drever-Hall technique [R. W. P. Dreyer, J. L. Hall, F. V. Kowalski, et al., “Laser phase and frequency stabilization using an optical resonator”, Appl. Phys. B 31(2), 97 (1983)] was used to lock laser emission to one transmission peak of the interferometer. To this end, the laser output was phase modulated and the intensity reflected by the interferometer was detected to generate a feedback signal to the semiconductor laser. Optical filtering occurred by transmission of the laser light through the interferometer. By implementing a double passage through the interferometer to enhance filtering, HALD et al obtained a noise reduction of −85 dB at 1 MHz. However, the experimental set-ups used were complex and bulky, not readily applicable to commercial applications.
There is thus a need for practical means and methods to reduce the white frequency noise of semiconductor lasers that preserve as much as possible their inherent is advantages while making them suitable for aforementioned high-end applications.